Evaluate: (0.064)$^{-\frac{1}{3}}$

Analyze the question: We need to evaluate 0.064 raised to the power −1/3. The negative sign means "take the reciprocal," and the 1/3 means "take the cube root."

Concept:

• a^(−n) = 1/aⁿ
• a^(1/3) = ∛a

Solution:

Step 1: Write 0.064 as a fraction. 0.064 = 64/1000

Step 2: Apply the negative power by flipping the fraction. (64/1000)^(−1/3) = (1000/64)^(1/3)

Step 3: Take the cube root of the numerator and denominator. ∛1000 = 10 and ∛64 = 4

So (1000/64)^(1/3) = 10/4

Step 4: Simplify. 10/4 = 5/2

Check: (2/5)³ = 8/125 = 0.064, so 0.064^(1/3) = 2/5. The negative power gives the reciprocal, 5/2. ✓

Tip: A negative power never makes the answer negative. It just flips the number. So options C and D can be eliminated immediately. Then remember that 0.064 = (0.4)³, so its cube root is 0.4 = 2/5, and the reciprocal is 5/2.